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51 pages, 976 KB  
Systematic Review
Variational Mechanics for Mining Infrastructure Design: A Systematic Review from Hamilton’s Principle to Physics-Constrained Optimization and Digital Twins
by Luis Rojas, Yuniel Martinez, Alex Paz, Alvaro Peña and José Garcia
Mathematics 2026, 14(4), 689; https://doi.org/10.3390/math14040689 (registering DOI) - 15 Feb 2026
Abstract
This article presents a systematic synthesis of variationally grounded approaches for the design and optimization of mining structural infrastructure. This study is motivated by the critical need to ensure stiffness, reliability, and operational availability under severe loading, mass constraints, and aggressive environmental conditions. [...] Read more.
This article presents a systematic synthesis of variationally grounded approaches for the design and optimization of mining structural infrastructure. This study is motivated by the critical need to ensure stiffness, reliability, and operational availability under severe loading, mass constraints, and aggressive environmental conditions. Methodologically, the study situates structural modeling and synthesis within the continuity of the principle of stationary action. It demonstrates that, in the quasi-static regime, structural equilibrium is obtained as the stationarity of the total potential energy; consequently, the finite element method (FEM) arises naturally as a Ritz–Galerkin approximation of this underlying variational statement. On this basis, topology optimization is interpreted as a physics-constrained optimization problem wherein the design is posed as an outer optimality level acting over an energetically defined state. It is worth noting that SIMP-based formulations require explicit regularization to define the effective problem being solved. Emphasis is placed on the traceability between physical assumptions, discretization choices, regularization, and the resulting structural interpretations. The core contribution of this paper is a systematic literature review that consolidates evidence across variational mechanics, FEM-based optimization, and industrial applications, identifying recurrent methodological patterns and gaps that currently limit transfer to mining practice. Furthermore, a fully specified illustrative case is included to demonstrate reporting discipline and methodological consistency, rather than as a validation of a new optimization method. The conclusions highlight that a variational reading provides a coherent theoretical backbone for structural analysis, synthesis, simulation, and physics-based digital twins, while also clarifying the extensions required for industrial deployment, such as stability constraints, manufacturability, and multiphysics coupling within Mining 4.0 workflows. Full article
(This article belongs to the Special Issue Advanced Computational Mechanics)
18 pages, 3883 KB  
Article
Study on Fracture Behavior of GH4169 Superalloy Considering Crack Closure Effect: Combining Numerical Modeling and BSL 3D DIC
by Zechang Li, Bin Kuang, Bin Wang, Xing Sun, Xinlong Yang, Bo Liu, Qihong Fang, Huimin Xie, Wei He and Yanhuai Ding
Appl. Sci. 2026, 16(4), 1944; https://doi.org/10.3390/app16041944 (registering DOI) - 15 Feb 2026
Abstract
As a critical aerospace structural material, the fatigue crack propagation behavior and fatigue life of the nickel-based GH4169 superalloy are directly related to the service safety of engineering components. The crack closure effect is one of the key factors influencing the fatigue life [...] Read more.
As a critical aerospace structural material, the fatigue crack propagation behavior and fatigue life of the nickel-based GH4169 superalloy are directly related to the service safety of engineering components. The crack closure effect is one of the key factors influencing the fatigue life of metallic materials. At present, the finite element method (FEM) is widely used to investigate fatigue crack propagation in metals. However, the commercial software ABAQUS 2021b employs the conventional Paris law for crack growth simulation, which neglects the influence of crack closure. In addition, ABAQUS cannot simultaneously perform fatigue life prediction and crack path prediction within a single numerical model. To overcome these limitations, the bi-prism-based single-lens (BSL) three-dimensional digital image correlation (3D DIC) technique was employed to experimentally investigate the crack closure behavior during fatigue crack propagation in GH4169 compact tension (CT) specimens. A new parameter, termed the crack opening ratio (COR), was introduced to quantitatively characterize the crack closure effect. Furthermore, a self-developed plugin was implemented on the ABAQUS platform through secondary development, enabling the numerical model to incorporate the influence of crack closure during fatigue crack propagation. The plugin automatically records the crack tip coordinates at each propagation step, calculates the stress intensity factors near the crack tip, and predicts the corresponding fatigue life, thereby integrating crack path prediction and fatigue life prediction within a unified framework. The results demonstrate that the COR effectively characterizes the crack closure effect in the numerical model, and the predicted fatigue life agrees with experimental results within an 11% deviation once the crack reaches a certain length. Full article
19 pages, 5211 KB  
Article
Predictions of Wear Performances of AlSi7Mg0.6 Cast Aluminum Alloy Under Different Displacement and Applied Load
by Guoqing Gu, Yun Ma, Fei Du and Aiguo Zhao
Materials 2026, 19(4), 752; https://doi.org/10.3390/ma19040752 (registering DOI) - 14 Feb 2026
Abstract
AlSi7Mg0.6 aluminum alloy is widely adopted in many industrial fields due to its favorable mechanical properties and lightweight merits. In the catenary system of high-speed railways, AlSi7Mg0.6 aluminum alloy is adopted as the substrate of the positioning hook and positioning support, which exhibit [...] Read more.
AlSi7Mg0.6 aluminum alloy is widely adopted in many industrial fields due to its favorable mechanical properties and lightweight merits. In the catenary system of high-speed railways, AlSi7Mg0.6 aluminum alloy is adopted as the substrate of the positioning hook and positioning support, which exhibit abnormal wear in some railways. Thus, it is very important to reveal the underlying wear characteristics and discover the key factors involved. In this study, the influences of displacement (0.5 mm, 1.5 mm, and 3.0 mm) and applied load (20 N, 50 N, 100 N, and 200 N) on the wear performance of AlSi7Mg0.6 aluminum alloy are investigated experimentally and numerically. Wear experiments are time-consuming and costly, but the finite element method (FEM) can effectively solve this problem. A UMESHMOTION user-defined subroutine integrated with an ABAQUS Arbitrary Lagrangian–Eulerian (ALE) adaptive mesh technique was developed to simulate the wear evolution process of the aluminum alloy under varying displacements and applied loads. The results indicate that the wear evolution process of AlSi7Mg0.6 aluminum alloy can be effectively simulated using the UMESHMOTION subroutine. The maximum wear depth (MWD) from the FEM deviates from the experimental results by no more than 10%, and the deviation is smaller than the experimental values. The largest deviation occurs when the displacement is 3.0 mm and the applied load is 100 N, where the discrepancy reaches 7.53%. The wear volume (WV) obtained from the FEM shows a deviation of less than 20% compared to experimental results. For the case with a displacement of 0.5 mm, the numerical results underestimate the wear volume, while for the case with displacements of 1.5 mm and 3.0 mm, the numerical results overestimate the wear volume. The largest deviation in this case occurs for the case with a displacement of 3.0 mm and applied loading of 100 N, with a discrepancy of 16.33%. Full article
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26 pages, 7179 KB  
Article
Determining Material Characteristics for Finite Element Simulations of Plastic Forming of the EN AW-7075 Aluminum Alloy
by Piotr Korczak, Bartłomiej Płonka, Dariusz Leśniak, Krzysztof Remsak and Konrad Żyłka
Metals 2026, 16(2), 219; https://doi.org/10.3390/met16020219 (registering DOI) - 14 Feb 2026
Abstract
FEM numerical analyses can be indicated as a common and basic tool used in the design of processes based on the plastic forming of metals. In such simulations, the accuracy of the results strongly depends on the quality of the material constitutive data [...] Read more.
FEM numerical analyses can be indicated as a common and basic tool used in the design of processes based on the plastic forming of metals. In such simulations, the accuracy of the results strongly depends on the quality of the material constitutive data used as the input. Good understanding of metals and their alloys’ deformation behavior, especially at hot working temperatures, is the key to developing or optimizing proper and economical processes. To provide reliable FEM simulation results, it is crucial to select an appropriate experimental method describing material behavior at elevated deformation temperatures. The most commonly method used for this is hot torsion tests, which can effectively provide a basis for developing constitutive models (for example, the Hensel–Spittel equation), but also produce the material constants needed to fully describe the behavior of the metal. This paper analyzes three experimental methods, compression testing, torsion testing, and spherical probe pressing, for determining material flow stress characteristics required for FEM simulations. The study focuses on the EN AW-7075 alloy, a high-strength aluminum alloy with limited hot workability. The methods were validated by comparing FEM predictions of extrusion force and profile temperature with results from industrial extrusion trials conducted on a 5 MN horizontal press. Full article
(This article belongs to the Section Computation and Simulation on Metals)
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29 pages, 2610 KB  
Article
Model-Agreement-Aware Multi-Objective Optimization for High-Frequency Transformers in EV Onboard Chargers
by Onur Kırcıoğlu and Sabri Çamur
Energies 2026, 19(4), 1000; https://doi.org/10.3390/en19041000 - 13 Feb 2026
Abstract
Developments in electric vehicle (EV) technology are pushing on-board chargers (OBCs) toward higher power density and efficiency, making high-frequency transformer loss prediction a critical design bottleneck. However, the accuracy of commonly used analytical winding-loss models varies strongly with frequency, conductor type (Litz/solid), window [...] Read more.
Developments in electric vehicle (EV) technology are pushing on-board chargers (OBCs) toward higher power density and efficiency, making high-frequency transformer loss prediction a critical design bottleneck. However, the accuracy of commonly used analytical winding-loss models varies strongly with frequency, conductor type (Litz/solid), window fill factor, and winding layout (e.g., interleaved), which can render single-model-based optimization unreliable. In this study, six analytical copper-loss models from the literature were independently reimplemented in a unified Python 3.11.5 workflow with a standardized interface to enable fair comparison under identical geometry and operating conditions. The models were benchmarked against 2D finite-element simulations on test scenarios with increasing physical complexity, including high fill-factor Litz windings and interleaved arrangements. The results confirm a regime-dependent behavior: no single model consistently outperforms others across the full design space, and model dispersion increases in geometrically stressed and higher-frequency regions. To manage this uncertainty, variance maps were generated and model disagreement was quantified using the coefficient of variation (CV). Finally, a reliability-oriented multi-objective optimization framework based on NSGA-II was developed, where a SmartTransformerRouter selects a reference loss estimate per candidate and CV is incorporated via constraints/penalties, with optional FEM triggering in high-uncertainty regions. Full article
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30 pages, 10747 KB  
Article
Digital Twin Framework for Cutterhead Design and Assembly Process Simulation Optimization for TBM
by Abubakar Sharafat, Waqas Arshad Tanoli, Sung-hoon Yoo and Jongwon Seo
Appl. Sci. 2026, 16(4), 1865; https://doi.org/10.3390/app16041865 - 13 Feb 2026
Viewed by 59
Abstract
With the rapid advancement in information technology, the digital twin and smart assembly process simulation have become an integral part of the design and manufacturing of high-precision products. However, conventional Tunnel Boring Machine (TBM) cutterhead design and on-site assembly planning remain largely experience-driven [...] Read more.
With the rapid advancement in information technology, the digital twin and smart assembly process simulation have become an integral part of the design and manufacturing of high-precision products. However, conventional Tunnel Boring Machine (TBM) cutterhead design and on-site assembly planning remain largely experience-driven and fragmented, with limited interoperability between geological characterization, structural verification, and constructability validation. This study proposes a digital twin-driven framework for TBM cutterhead design optimization and assembly process simulation that integrates geology-aware design inputs, BIM-based information modelling, FEM-based structural assessment, and immersive virtual environments within a unified virtual–physical workflow. To ensure consistent data exchange across platforms, an IFC4.3-compliant ontology is established using a non-intrusive property-set (Pset) extension strategy to represent cutterhead components, geological parameters, FEM load cases/results, and assembly tasks. Tunnel-scale stress analysis and cutter–rock interaction modelling are used to define project-representative cutter loading envelopes, which are mapped to a high-fidelity cutterhead FEM model for iterative structural refinement. The optimized configuration is then transferred to a game-engine/VR environment to support full-scale design inspection and assembly rehearsal, followed by manufacturing and field deployment with bidirectional feedback. To validate the proposed framework, an implementation case study of a deep hard-rock tunnelling project is presented where five design iterations were tracked across BIM–FEM–VR and nine constructability issues detected and resolved prior to assembly. The results indicate that the proposed digital twin approach strengthens traceability from geology to loading to structural response, reduces localized stress concentration at critical interfaces, and improves assembly readiness for complex tunnelling projects. Full article
(This article belongs to the Special Issue Surface and Underground Mining Technology and Sustainability)
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23 pages, 2606 KB  
Article
A Proof-of-Concept Framework Integrating ML-Based MRI Segmentation with FEM for Transfemoral Residual Limb Modelling
by Ryota Sayama, Yukio Agarie, Hironori Suda, Hiroshi Otsuka, Kengo Ohnishi, Shinichiro Kon, Akihiko Hanahusa, Motoki Takagi and Shinichiro Yamamoto
Prosthesis 2026, 8(2), 16; https://doi.org/10.3390/prosthesis8020016 - 13 Feb 2026
Viewed by 67
Abstract
Background: Accurate evaluation of pressure distribution at the socket–limb interface is essential for improving prosthetic fit and comfort in transfemoral amputees. This study aimed to develop a proof-of-concept framework that integrates machine learning–based segmentation with the finite element method (FEM) to explore the [...] Read more.
Background: Accurate evaluation of pressure distribution at the socket–limb interface is essential for improving prosthetic fit and comfort in transfemoral amputees. This study aimed to develop a proof-of-concept framework that integrates machine learning–based segmentation with the finite element method (FEM) to explore the feasibility of an initial workflow for residual-limb analysis during socket application. Methods: MRI data from a transfemoral amputee were processed using a custom image segmentation algorithm to extract adipose tissue, femur, and ischium, achieving high F-measure scores. The segmented tissues were reconstructed into 3D models, refined through outlier removal and surface smoothing, and used for FEM simulations in LS-DYNA. Pressure values were extracted at nine sensor locations and compared with experimental measurements to provide a preliminary qualitative assessment of model behaviour. Results: The results showed consistent polarity between measured and simulated values across all points. Moderate correspondence was observed at eight low-pressure locations, whereas a substantial discrepancy occurred at the ischial tuberosity (IS), the primary load-bearing site. This discrepancy likely reflects the combined influence of geometric deviation in the reconstructed ischium and the non-physiological medial boundary condition required to prevent unrealistic tissue displacement. This limitation indicates that the current formulation does not support reliable quantitative interpretation at clinically critical locations. Conclusions: Overall, the proposed framework provides an initial demonstration of the methodological feasibility of combining automated anatomical modeling with FEM for exploratory pressure evaluation, indicating that such an integrated pipeline may serve as a useful foundation for future development. While extensive refinement and validation are required before any quantitative or clinically meaningful application is possible, this work represents an early step toward more advanced computational investigations of transfemoral socket–limb interaction. Full article
(This article belongs to the Special Issue Finite Element Analysis in Prosthesis and Orthosis Research)
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20 pages, 5587 KB  
Article
Fourier Neural Operators for Fast Multi-Physics Sensor Response Prediction: Applications in Thermal, Acoustic, and Flow Measurement Systems
by Ali Sayghe, Mohammed Mousa, Salem Batiyah and Abdulrahman Husawi
Sensors 2026, 26(4), 1165; https://doi.org/10.3390/s26041165 - 11 Feb 2026
Viewed by 80
Abstract
Accurate and rapid prediction of sensor responses is critical for real-time measurement systems, digital twin implementations, and sensor design optimization. Traditional numerical methods such as Finite Element Method (FEM) and Computational Fluid Dynamics (CFD) provide high-fidelity solutions but suffer from prohibitive computational costs, [...] Read more.
Accurate and rapid prediction of sensor responses is critical for real-time measurement systems, digital twin implementations, and sensor design optimization. Traditional numerical methods such as Finite Element Method (FEM) and Computational Fluid Dynamics (CFD) provide high-fidelity solutions but suffer from prohibitive computational costs, limiting their applicability in time-sensitive applications. This paper presents a novel framework utilizing Fourier Neural Operators (FNO) as surrogate models for fast multi-physics sensor response prediction across thermal, acoustic, and flow measurement domains. Unlike conventional neural networks that learn finite-dimensional mappings, FNO learns operators between infinite-dimensional function spaces by parameterizing the integral kernel in Fourier space, enabling resolution-invariant predictions with remarkable computational efficiency. We demonstrate the framework’s efficacy through three comprehensive case studies: (1) thermal sensor response prediction achieving R2>0.98 with 8300× speedup over FEM, (2) acoustic sensor array modeling with mean absolute error below 0.5 dB and 4000× speedup over BEM, and (3) flow sensor characterization with velocity field prediction accuracy exceeding 97% and 31,000× speedup over CFD. The proposed FNO-based surrogate models are trained on simulation datasets generated from high-fidelity numerical solvers and validated against simulation holdout data for all three case studies, with additional experimental validation conducted for the thermal sensor case. Results indicate that FNO architectures effectively capture the underlying physics governing sensor behavior while reducing inference time from minutes to milliseconds. The framework enables real-time sensor calibration, uncertainty quantification, and design optimization, opening new possibilities for intelligent measurement systems and Industry 4.0 applications. We also investigate the spectral characteristics of FNO predictions, addressing the inherent low-frequency bias through a hybrid architecture combining FNO with local convolutional layers. The primary contributions of this work include: (1) the first systematic application of FNO-based surrogate modeling specifically tailored for sensor response prediction across multiple physics domains, (2) a novel H-FNO architecture that combines spectral operators with local convolutions to mitigate spectral bias in sensor applications, and (3) comprehensive validation including both simulation and experimental data for practical deployment. This work establishes FNO as a powerful tool for accelerating sensor simulation and advancing the field of AI-enhanced instrumentation and measurement. Full article
(This article belongs to the Section Physical Sensors)
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23 pages, 2456 KB  
Article
Research on Intelligent Thermal Optimization for Chiplet-Based Heterogeneously Integrated AI Chip Embedded with Leaf-Vein-Inspired Fractal Microchannels
by Jie Wu, Yu Liang, Guibin Liu, Ruiyang Pang, Yi Teng, Chen Li, Xuetian Bao, Shi Lei and Zhikuang Cai
Materials 2026, 19(4), 679; https://doi.org/10.3390/ma19040679 - 10 Feb 2026
Viewed by 153
Abstract
Conventional cooling schemes that rely on rigid heat-sink-to-die coupling in vertical stacks fail to track the dynamic, non-uniform heat map of high-performance artificial-intelligence (AI) chips employing chiplet-based heterogeneous integration, giving rise to local hot spots. To eliminate this mismatch, we present a leaf-vein-inspired [...] Read more.
Conventional cooling schemes that rely on rigid heat-sink-to-die coupling in vertical stacks fail to track the dynamic, non-uniform heat map of high-performance artificial-intelligence (AI) chips employing chiplet-based heterogeneous integration, giving rise to local hot spots. To eliminate this mismatch, we present a leaf-vein-inspired fractal microchannel tailored for such AI processors. Its hierarchical bifurcation–confluence topology adaptively reshapes the flow field, delivering ultra-low thermal resistance, high heat-transfer coefficients, and uniform dissipation. Coupled with reconfigurable chiplet placement, the design is evaluated through FEM-based orthogonal experiments that rank the influence of coolant, channel diameter/depth, inlet/outlet position, substrate thickness, and flow rate via range analysis and Analysis of Variance (ANOVA). A machine-learned surrogate model of junction temperature is then fed to Particle Swarm Optimization (PSO) for multi-parameter optimization. When re-simulated with the optimal parameter set, the symmetric fractal network lowered the AI chip junction temperature from 127.80 °C to 30.97 °C, a 76% improvement, offering a theoretical basis for hotspot mitigation in advanced heterogeneous AI packages. Full article
(This article belongs to the Special Issue Microstructural and Mechanical Characteristics of Welded Joints)
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25 pages, 3150 KB  
Article
Electromagnetic and Modeling of Induction Furnaces Using Finite Element Methods
by Ghada Mahmoud Ibrahim, Asmaa Sobhy Sabik and Adel Saad Nada
Magnetism 2026, 6(1), 9; https://doi.org/10.3390/magnetism6010009 - 10 Feb 2026
Viewed by 135
Abstract
This paper presents a comparative modeling and analysis of an induction furnace for melting aluminum (Al) and copper (Cu), focusing on their electromagnetic behavior and heating performance. The study employs ANSYS Maxwell software version 16.0 with the finite element method (FEM) to simulate [...] Read more.
This paper presents a comparative modeling and analysis of an induction furnace for melting aluminum (Al) and copper (Cu), focusing on their electromagnetic behavior and heating performance. The study employs ANSYS Maxwell software version 16.0 with the finite element method (FEM) to simulate eddy current generation, Joule heating, and current density distribution in the metallic workpieces. The effects of coil geometry, input current, and operating frequency (50–100 kHz) on heating efficiency and skin depth are investigated. Estimated heating times based on ohmic losses are provided, revealing significant differences between aluminum and copper due to their distinct electrical and thermal properties. The results demonstrate that higher frequencies concentrate heating near the surface, reducing skin depth, while copper exhibits more uniform heating than aluminum. These findings offer practical insights for optimizing induction furnace design and operation for different non-ferrous metals. Full article
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18 pages, 3577 KB  
Article
Design and Comparative Analysis of a Cryo-Cooling System of a Performance Evaluation System for a HTS Field Coil
by Byeong-Soo Go and Seok-Ju Lee
Energies 2026, 19(4), 912; https://doi.org/10.3390/en19040912 - 9 Feb 2026
Viewed by 171
Abstract
High-temperature superconducting (HTS) technologies continue to advance as promising solutions for large-capacity rotating electrical machinery. However, the cryogenic architecture required to maintain superconducting states remains a critical design challenge, particularly for performance evaluation systems (PESs). Conventional helium–neon (He–Ne) circulation-based cooling enables stable low-temperature [...] Read more.
High-temperature superconducting (HTS) technologies continue to advance as promising solutions for large-capacity rotating electrical machinery. However, the cryogenic architecture required to maintain superconducting states remains a critical design challenge, particularly for performance evaluation systems (PESs). Conventional helium–neon (He–Ne) circulation-based cooling enables stable low-temperature operation and has been experimentally validated in previous PES implementations, but it introduces substantial limitations due to installation complexity, flow-induced instability, and limited adaptability to different coil configurations. To address these constraints, this study proposes a conduction-cooled PES architecture optimized for HTS field coil testing and examines its thermal and structural characteristics through comprehensive design and finite element method (FEM)-based analysis. A multi-stage conduction cooling pathway using a cryocooler, thermal straps, and copper heat plates was designed to achieve uniform temperature distribution and reduce thermal gradients across the HTS winding. Three-dimensional FEM simulations were performed to evaluate the steady-state temperature distribution and heat-transfer characteristics of the proposed conduction-cooled PES under representative thermal load conditions, and the predicted cooling performance was comparatively assessed against the He–Ne cooled PES. The conduction-cooled PES was analyzed by comparing its predicted performance with previously obtained experimental results from the He–Ne cooled PES. The proposed conduction cooling architecture achieved a significant reduction in total heat load, decreasing from 177 W in the He–Ne system to approximately 78 W in the conduction-cooled configuration while also improving thermal efficiency and simplifying system integration. In addition, conduction cooling enhances compatibility with a wider range of HTS coil geometries by eliminating the constraints associated with fluid-based circulation. While the proposed conduction-cooled PES has not yet been physically fabricated, the numerical framework was established based on experimentally confirmed operating conditions of the previously implemented He–Ne-cooled PES, and future work will include fabrication and experimental validation of the conduction-cooled configuration. These findings demonstrate that conduction cooling represents a practical and scalable alternative for next-generation PES platforms and provide essential design guidelines for the development of high-field HTS coils and large-capacity superconducting rotating machines. Full article
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23 pages, 2768 KB  
Article
Enhancing Permanent Magnet Sliding Bearings Through Multi-Layer Yoke for Minimized Magnetic Leakage
by Yong Liu, Haitao Zhao, Jixing Li, Lei Wu and Yang Xia
Materials 2026, 19(3), 642; https://doi.org/10.3390/ma19030642 - 6 Feb 2026
Viewed by 251
Abstract
To mitigate the potential adverse effects of magnetic flux leakage from permanent-magnet sliding bearings on human health and the environment, this study proposes a leakage-suppressed design based on a multi-layer yoke configuration. The magnetic performance of the bearing was systematically investigated using finite [...] Read more.
To mitigate the potential adverse effects of magnetic flux leakage from permanent-magnet sliding bearings on human health and the environment, this study proposes a leakage-suppressed design based on a multi-layer yoke configuration. The magnetic performance of the bearing was systematically investigated using finite element method (FEM) simulations. The results demonstrate a pronounced reduction in magnetic leakage when replacing a conventional single-layer yoke with an optimized multi-layer yoke structure. Targeted design refinements, including optimization of both the number and angular span of magnetic rings, as well as tuning of the yoke thickness, further enhance the effectiveness of the leakage-suppression strategy. The proposed multi-layer yoke configuration preserves both the magnetic force and the load-carrying capacity of the magnetic bearing, while concurrently providing a viable theoretical and engineering basis for the design and structural optimization of leakage-controlled permanent-magnet bearings. Full article
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18 pages, 4185 KB  
Article
Design of a Vibration Energy Harvester Powered by Machine Vibrations for Variable Frequencies and Accelerations
by Axel Wellendorf, Leonard Klemenz, Sebastian Trampnau, Anton Güthenke, Jan Madalinski, Nils Landefeld and Joachim Uhl
J. Exp. Theor. Anal. 2026, 4(1), 7; https://doi.org/10.3390/jeta4010007 - 5 Feb 2026
Viewed by 208
Abstract
A vibration energy harvester (VEH) based on the principle of variable magnetic reluctance has been developed to enable wireless and maintenance-free power supply for condition monitoring sensors in vibrating machinery. Conventional battery or wired solutions are often impractical due to limited lifetime and [...] Read more.
A vibration energy harvester (VEH) based on the principle of variable magnetic reluctance has been developed to enable wireless and maintenance-free power supply for condition monitoring sensors in vibrating machinery. Conventional battery or wired solutions are often impractical due to limited lifetime and high installation costs, motivating the use of vibration-based energy harvesting. The proposed VEH converts mechanical vibrations into electrical energy through the relative motion of a movable ferromagnetic core within a magnetic circuit. Unlike conventional VEH designs, where the magnet is the moving element, this concept utilizes a movable ferromagnetic core in combination with a stationary pole piece for voltage induction. This configuration enables a compact and easily adjustable proof mass, as neither the coil nor the magnet needs to be moved. The VEH is designed to operate effectively under excitation frequencies between 16 Hz and 50 Hz and acceleration levels from 9.81 ms2 (equivalent to 1 g) up to 98.1 ms2 (equivalent to 10 g). To ensure a reliable power supply, the VEH must deliver a minimum electrical output of 0.1 mW at the lowest excitation (1 g) while maintaining structural integrity. Additionally, the maximum permissible displacement amplitude of the movable core is limited to 1.15 mm to avoid mechanical damage and ensure durability over long-term operation. Coupled magnetic-transient and mechanical finite element method (FEM) simulations were conducted to analyze the system’s dynamic behavior and electrical power output across varying excitation frequencies and accelerations. A laboratory prototype was developed and tested under controlled vibration conditions to validate the simulation results. The experimental measurements confirm that the VEH achieves an electrical output of 0.166 mW at 9.81 ms2 and 16 Hz, while maintaining the maximum allowable displacement amplitude of 1.15 mm, even at 98.1 ms2 (10 g) and 50 Hz. The strong agreement between simulation and experimental data demonstrates the reliability of the coupled FEM approach. Overall, the proposed VEH design meets the defined performance targets and provides a robust solution for powering wireless sensor systems under a wide range of vibration conditions. Full article
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13 pages, 7941 KB  
Article
Modelling Eddy Current Testing of Gaps in Carbon Fibre Structures Based on Spline Approximation
by Till Schulze, Maren Rake, Dirk Hofmann, Johannes Mersch, Martin Schulze, Chokri Cherif and Henning Heuer
Sensors 2026, 26(3), 1032; https://doi.org/10.3390/s26031032 - 5 Feb 2026
Viewed by 192
Abstract
Defects such as gaps, delamination, and the misalignment of fibres impair the performance of carbon fibre-reinforced composites and can lead to structural failure during operation. Eddy current testing has proven to be a suitable method for detecting these defects early in the manufacturing [...] Read more.
Defects such as gaps, delamination, and the misalignment of fibres impair the performance of carbon fibre-reinforced composites and can lead to structural failure during operation. Eddy current testing has proven to be a suitable method for detecting these defects early in the manufacturing process. However, validated electromagnetic modelling techniques are required to develop new eddy current sensors and gain a better understanding of the eddy current signals caused by different defect sizes. This paper proposes a novel finite element modelling approach to better account for fibre heterogeneity using spline approximation. Further, adaptive mesh refinement is used to reduce FEM solution errors. A defect in the form of a gap is modelled by adjusting the spline approximation accordingly. Finally, the model also accounts for inter-laminar current paths between carbon fibre layers, which are determined by four-terminal resistance measurement. The results show that the electromagnetic properties of the structure can be successfully modelled. The simulation is validated by comparing the virtual scans with eddy current scans of dry carbon fibre fabric with and without artificially manufactured gaps. Full article
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17 pages, 2537 KB  
Article
Numerical Analysis of In-Plane Stiffness of Light-Timber-Framed Wall Elements with Various Sheathing Materials
by Jelena Vilotijević and Miroslav Premrov
Buildings 2026, 16(3), 629; https://doi.org/10.3390/buildings16030629 - 2 Feb 2026
Viewed by 127
Abstract
This paper numerically analyses numerous parameters with the most sensitive impact on the in-plane lateral behaviour of light timber-framed (LTF) wall elements. Different types of sheathing material (fibre-plaster boards, OSB) are studied according to the parametrically chosen distance between the fasteners, using three [...] Read more.
This paper numerically analyses numerous parameters with the most sensitive impact on the in-plane lateral behaviour of light timber-framed (LTF) wall elements. Different types of sheathing material (fibre-plaster boards, OSB) are studied according to the parametrically chosen distance between the fasteners, using three different calculation procedures: (a) a previously developed semi-analytical procedure using the Modified Gamma Method (MGM) accounts for bending, shear, and timber-to-framing connection flexibility simultaneously; (b) a previously developed FEM Spring Model as the most accurate approach; and (c) in this study, a specially developed innovative FEM 2D Hinge Model using the two-dimensional hinge layer to simulate the deformability between the sheathing boards and the timber frame, which enables significantly faster FEM analysis compared to the already developed FEM Spring Model. This, in turn, realistically allows for much faster analysis of real multi-storey timber structures. In order to only judge the influence of the sheathing material and fastener disposition, in all cases, the tensile and compressive vertical supports are considered to be stiff-supported wall elements as prescribed by the valid Eurocode 5 standard; however, it is possible to additionally include all three possible supporting flexibilities. The study places particular emphasis on the deformation of sliding fasteners between the sheathing boards and the timber frame, which arises from fastener flexibility and can significantly reduce the overall in-plane stiffness of LTF wall elements. For specially selected parametric values of fastener spacing (s = 20, 37.5, 75, and 150 mm), parametric FEM analysis using a special 2D hinge layer is additionally developed and performed to validate the previously developed semi-analytical expressions by the MGM for the in-plane wall stiffness, which seems to be the most appropriate for designing engineering implementation. All applied approaches to modelling wall elements considered the same parameters for evaluating the stiffness of an individual wall element, which represents a fundamental input parameter in the modelling of frame wall elements within the overall structure. The aim of the study is to determine the most suitable and accurate model, as the response of the entire structure to horizontal loading depends on the design of the individual wall element. Among these, it has been demonstrated that the thickness of the load-bearing timber frame and the type of resisting LTF walls (internal or external) have practically no significant effect on the in-plane stiffness of such wall elements. Consequently, the type of sheathing material (FPB or OSB) and especially the spacing between the fasteners are much more sensitive parameters, which would probably need to be given further consideration in future FEM studies. Full article
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